Geodesic
On semi cover-avoiding or $S$-quasinormally embedded subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 1 (2014), pp. 57-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we characterize the nilpotency and supersolvability of a finite group $G$ by assuming some subgroups of prime power order are either semi cover-avoiding or $S$-quasinormally embeded in $G$. Some known results are generalized.
Keywords: semi cover-avoiding subgroup; $S$-quasinormally embeded subgroup; $p$-nilpotent group; supersolvable group. 
@article{PFMT_2014_1_a9,
     author = {Abid Mahboob and Lijun Huo and Jinghua Lu},
     title = {On semi cover-avoiding or $S$-quasinormally embedded subgroups of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {57--62},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_1_a9/}
}
TY  - JOUR
AU  - Abid Mahboob
AU  - Lijun Huo
AU  - Jinghua Lu
TI  - On semi cover-avoiding or $S$-quasinormally embedded subgroups of finite groups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2014
SP  - 57
EP  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2014_1_a9/
LA  - en
ID  - PFMT_2014_1_a9
ER  - 
%0 Journal Article
%A Abid Mahboob
%A Lijun Huo
%A Jinghua Lu
%T On semi cover-avoiding or $S$-quasinormally embedded subgroups of finite groups
%J Problemy fiziki, matematiki i tehniki
%D 2014
%P 57-62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2014_1_a9/
%G en
%F PFMT_2014_1_a9
Abid Mahboob; Lijun Huo; Jinghua Lu. On semi cover-avoiding or $S$-quasinormally embedded subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 1 (2014), pp. 57-62. http://geodesic.mathdoc.fr/item/PFMT_2014_1_a9/

[1] M. Asaad, A. A. Heliel, “On $S$-quasinormally embedded subgroups of finite groups”, J. Pure. Appl. Algebra, 165 (2001), 129–135 | DOI | MR | Zbl

[2] M. Asaad, A. A. Heliel, M. Ezzat Mohamed, “Finite groups with some subgroups of prime power order $S$-quasinormally embedded”, Comm. Algebra, 32:5 (2004), 2019–2027 | DOI | MR | Zbl

[3] A. Ballester-Bolinches, M. C. Pedraza-Aquilera, “Sufficient conditions for supersolubility of finite group”, J. Pure Appl. Algebra, 127:2 (1998), 113–118 | DOI | MR | Zbl

[4] W. E. Deskins, “On quasinormal subgroups of finite groups”, Math. Z., 82 (1963), 125–132 | DOI | MR | Zbl

[5] Y. Fan, X. Guo, K. P. Shum, “Remarks on two generalizations of normality of subgroups”, Chinese Ann. Math. Ser. A, 27:2 (2006), 169–176 | DOI | MR | Zbl

[6] W. Gaschütz, “Praefrattinigruppen”, Arch. Math. (Basel), 13 (1962), 418–426 | DOI | MR | Zbl

[7] J. D. Gillam, “Cover-avoid subgroups in finite solvable groups”, J. Algebra, 29 (1974), 324–329 | DOI | MR | Zbl

[8] D. Gorenstein, Finite Groups, Harper Row Publishers, New York–Evanston–London, 1968 | MR | Zbl

[9] W. Guo, The Theory of Class of Groups, Science Press-Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000 | MR

[10] X. Guo, L. Wang, “On finite groups with some semi cover-avoiding subgroups”, Acta Math Sinica. English Series, 23 (2007), 1689–1696 | DOI | MR | Zbl

[11] X. Guo, P. Guo, K. P. Shum, “On semi cover-avoiding subgroups of finite group”, J. Pure Appl. Algebra, 209 (2007), 151–158 | DOI | MR | Zbl

[12] X. Guo, K. P. Shum, “Cover-avoidance properties and the structure of finite groups”, J. Pure Appl. Algebra, 181:2–3 (2003), 297–308 | MR

[13] B. Huppert, Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[14] O. H. Kegel, “Sylow gruppen und subnormalteiler endlicher gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[15] Y. Li, “Finite groups with some $S$-quasinormally embedded subgroups”, Comm. Algebra, 38:11 (2010), 4202–4211 | DOI | MR | Zbl

[16] X. Li, Y. Yang, “Semi $CAP$-subgroups and the structure of finite groups”, Acta Math. Sin., 51 (2008), 1181–1187 | MR

[17] Y. Li, Y. Wang, H. Wei, “On $p$-nilpotency of finite groups with some subgroups $\pi$-quasinormally embedded”, Acta Math Hungarica, 108:4 (2005), 283–298 | DOI | MR | Zbl

[18] J. Petrillo, “$CAP$-subgroups in a direct product of finite groups”, J. Algebra, 306:2 (2006), 432–438 | DOI | MR | Zbl

[19] D. J. S. Robinson, A Course in the Theory of Groups, Springer-Verlag, New-York–Heidelberg–Berlin, 1982 | MR | Zbl

[20] P. Schmid, “Subgroups permutable with all Sylow subgroups”, J. Algebra, 207 (1998), 285–293 | DOI | MR | Zbl

[21] A. N. Skiba, “On weakly $s$-permutable subgroups of finite groups”, J. Algebra, 315 (2007), 192–209 | DOI | MR | Zbl

[22] M. J. Tomkinson, “Cover-avoidance properties in finite soluble groups”, Canad. Math. Bull., 19:2 (1976), 213–216 | DOI | MR | Zbl

[23] J. G. Thompson, “Normal $p$-complements for finite groups”, J. Algebra, 1 (1964), 43–46 | DOI | MR | Zbl

[24] H. Wei, Y. Wang, “On $c^*$-normality and its properties”, J. Group Theory, 10 (2007), 211–223 | DOI | MR | Zbl

[25] T. Zhao, X. Li, “Semi cover-avoiding properties of finite groups”, Front. Math. China, 5:4 (2010), 793–800 | DOI | MR | Zbl